1. Geometry
MSM2

2. If we look around us, we will see angles everywhere.
Angles In Daily Life
If we look around us, we will see angles everywhere.

3. Naming An Angle A B C For example: ÐABC or ÐCBA
To name an angle, we name any point on one ray, then the vertex, and then any point on the other ray. A B C
For example: ÐABC or ÐCBA
We may also name this angle only by the single letter of the vertex, for example ÐB.

4. Adjacent angles are “side by side” and share a common ray.
15º
45º

5. These are examples of adjacent angles.
45º
80º
35º
55º
130º
50º
85º
20º

6. These angles are NOT adjacent.
100º
50º
35º
35º
55º
45º

7. Complementary angles add up to 90º.
30º
40º
50º
60º
Adjacent and Complementary Angles
Complementary Angles but not Adjacent

8. Complementary Angles sum to 90°
50°
40°

9. 1) Find the missing angle.?°
36°

10. Supplementary Angles sum to 180°
150°
30°

11. Supplementary angles add up to 180º.
40º
120º
60º
140º
Adjacent and Supplementary Angles
Supplementary Angles but not Adjacent

12. 6) Find the missing angle.?°
58°

13. Congruent Angles A B C D E F D E F
Two angles that have the same measure are called congruent angles. A B C
300 D E F
300 D E F
300
Congruent angles have the same size and shape.

14. Vertically Opposite Angles
Vertically opposite angles are pairs of angles formed by two lines intersecting at a point. A D B C
ÐAPC = ÐBPD P
ÐAPB = ÐCPD
Four angles are formed at the point of intersection.
Vertically opposite angles are congruent.
Point of intersection ‘P’ is the common vertex of the four angles.

15. Vertical Angles are opposite one another. Vertical angles are congruent.
100°
100°

16. Vertical Angles are opposite one another. Vertical angles are congruent.
80°
80°

17. Adjacent angles: ÐAPC and ÐCPD
Name the vertically opposite angles and adjacent angles in the given figure: A D B C P
Vertically opposite angles: ÐAPC and ÐBPD
Adjacent angles: ÐAPC and ÐCPD
ÐAPB and ÐCPD
ÐAPB and ÐBPD

19. Find the missing angles

20. Pairs Of Angles Formed by a Transversal
Corresponding angles
Alternate angles
Interior angles

21. Pairs Of Angles Formed by a Transversal
A line that intersects two or more lines at different points is called a transversal. G F
Line L (transversal)
Line M B A P
Line N D C Q
Four angles are formed at point P and another four at point Q by the transversal L.
Line M and line N are parallel lines.
Line L intersects line M and line N at point P and Q.
Eight angles are formed in all by the transversal L.

22. Interior and exterior parts

23. Corresponding angles
When two lines are crossed by the transversal the angles in matching corners are called corresponding angles.

24. Corresponding angles You need a pair of parallel lines. corresponding
Draw any line to cut the pair of parallel lines.
What angle is the same as the red one?

25. How do you tell angles are corresponding?
Look for a letter F in any orientation.

26. Alternate interior angles
Alternate Interior angles are two nonadjacent interior angles that lie on opposite sides of a transversal.

27. Alternate Exterior angles
Alternate Exterior angles are the angle pairs that are on the outsides of the two lines (the exterior) and on opposite (or alternate sides) of the transversal.

28. Alternate interior angles
You need a pair of parallel lines.
Alternate
interior angles
Draw any line to cut the pair of parallel lines.
What angle is the same as the blue one?

29. How do you tell angles are alternate interior ?
interior angles
Look for a letter Z in any orientation.

30. Name the pair of alternate interior and exterior angles?

31. Practice Time!

32. WHY?? Angle 2 measures 110°. What do the other angles measure? 1. 2.3. 4. 5. 6. 7. 8.
WHY??

33. 1) Find the missing angle.?°
36°

34. 1) Find the missing angle.?°
36°

35. 1) Find the missing angle.?°
36°
90 ° – 36 = 54°

36. 2) Find the missing angle.?°
64°

37. 2) Find the missing angle.?°
64°
90 ° – 64° = 26°

38. 3) Solve for x.
2x°
3x°

39. 3) Solve for x.
2x°
3x°
3x° + 2x° = 90°
5x = 90
x =18

40. 4) Solve for x.
x + 25
2x + 5

41. 4) Solve for x. x + 25 2x + 5 (2x + 5) + (x + 25) = 90 3x + 30 = 90

42. 5) Find the missing angle.
168° ?°

43. 5) Find the missing angle.
168° ?°
180° – 168° = 12°

44. 6) Find the missing angle.?°
58°
180° – 58° = 122°

45. 7) Solve for x. 5x 4x

46. 7) Solve for x. 5x 4x
4x + 5x = 180
9x = 180
x = 20

47. 8) Solve for x.
3x + 20
2x + 10